The United States and Japan will step up their defence cooperation to deal with the threat from nuclear-armed North Korea as tensions in East Asia remain high, officials from the two allies said on Thursday.

Day of sorrow and healing after siege

Tears have flowed in private and in public for victims of the Sydney cafe siege Tori Johnson and Katrina Dawson, as Sydney continues the business of healing from the horror.

One week on from the Martin Place siege, hundreds of family and friends farewelled Mr Johnson at a private funeral on Tuesday morning, in a church just 100 metres from the siege site in the centre of Sydney.

Mr Johnson was hailed as a hero for trying to wrest the gun from Man Haron Monis, who took 18 people hostage in the Lindt Cafe on the morning of December 15. It was an act that cost the cafe manager his life.

Ms Dawson lost her life in the violent conclusion to the siege in the early hours of December 16.

Sunflowers covered 34-year-old Mr Johnson's white coffin as it was carried to a white hearse while his father, Ken, was consoled by NSW Police Commissioner Andrew Scipione as he wept outside the church.

NSW Premier Mike Baird and NSW Governor David Hurley also attended the funeral.

A few hours later, more than 1000 people filled halls to overflowing at the University of Sydney at a public memorial service for Ms Dawson, described as a celebration of the vivacious 38-year-old barrister and mother of three's life.

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Tears flowed as tribute after tribute revealed the depth of the loss felt by her family, friends and the broader community in the terror of last week.

Ms Dawson's university friends remembered her as having a wicked sense of humour, an ever-ready smile and a plentiful supply of hugs and champagne.

Leading barrister Jeremy Stoljar SC described Ms Dawson as a supremely talented practitioner of the law who was always formidably prepared but unfailingly polite in the courtroom.

And, as Ms Dawson's parents Sandy and Jane, husband Paul Smith, brothers Sandy and Angus and her friends spoke, all remembered her as a devoted mother for whom family always came first.

Former Governor-General Dame Quentin Bryce, who first met Ms Dawson when the talented university student came under her care when she was principal of The Women's College at Sydney University, told the gathering: "Our country has lost a shining star".

Ms Dawson's heartbroken brother, Angus, said in a poem to his sister: "It can't be you".

Survivors of the hostage ordeal attended both services, with Joel Herat among those at Mr Johnson's funeral and John O'Brien in the crowd at Ms Dawson's service.

Fellow survivor and Ms Dawson's close friend, Julie Taylor, read a poem Ms Dawson had written to her husband for their wedding in 2001.

Mr Smith read a eulogy to the woman he knew was his perfect match when they met as young law students. It included words from their three children - four-year-old Sasha, six-year-old Ollie and eight-year-old Chloe. They also chose the songs played at the service.

The Kenny Rogers classic, The Gambler, was chosen by Chloe because of her mother's love of country music and singer Troy Cassar-Daley led the rendition.

The huge floral tribute to Mr Johnson and Ms Dawson that has covered much of Martin Place was removed on Tuesday morning, ahead of expected rain.

A smaller tribute site has been established under a marquee in Martin Place where a group of siege survivors placed flowers after Mr Johnson's funeral.